Two-magnon states in a one-dimensional non-Heisenberg ferromagnet of spins = 1 with interactions up to third neighbors

Abstract

We consider a two-magnon system in a one-dimensional non-Heisenberg ferromagnet of spin s = 1 with interactions of nearest, second, and third neighbors. We prove that for Λ = π and J = J1, the system has a unique two-magnon bound state (TMBS), while for Λ = π and J = 2J1, the system has three bound states. If Λ = π and J ≠ J1, J ≠ 2J1, the system has at most five TMBS. The energies of these bound states are evaluated.